Final answer:
To write the repeating decimal 0.1717... as a fraction, we can use the concept of infinite geometric series. The repeating decimal 0.1717... can be written as the fraction 17/99.
Step-by-step explanation:
To write the repeating decimal 0.1717... as a fraction, we can use the concept of infinite geometric series. Let's represent the repeating part of the decimal as a variable.
Let x = 0.171717...
Multiplying both sides by 100, we get 100x = 17.171717...
Subtracting the original equation from the multiplied equation eliminates the repeating part, so 100x - x = 17.171717... - 0.171717...
Simplifying, we have 99x = 17.
Dividing both sides by 99, we find that x = 17/99.
Therefore, the repeating decimal 0.1717... can be written as the fraction 17/99.
Learn more about Repeating Decimals